Your question isn't easily answered, since there are so many variables. There are all sorts of telephone+internet packages available, so you could pay anywhere from 30 to 50 euros per month + long distance calls. Being in a rural area you will find your selection of internet providers a bit limited. Where I am, for example, only Deutsche Telekom will hook up a DSL connection, and I can't get anything faster than DSL1000. Your available speed choices will also impact price. Make sure you go for flat rate internet.
Be careful which cell phone provider you decide to go with. Coverage in rural areas can be problematic. In my last apartment, only Vodafone D2 was accessable. Friends with other providers got weak or no signal in my village. So first find out which networks are best for your area. Then decide whether you prefer a 2-year contract with regular minimum monthly fees, or a pay-as-you-go cell phone.
Grocery prices can vary quite a bit, depending on where you shop, what products you buy, and if you pay attention to sales. You'll most likely be going to
Aldi,
Lidl or
Kaufland. See their web sites for an idea of prices.
Car insurance depends on your age, your driving record, and your car. Make sure that you bring all your insurance & driving records when you come over, and go to an insurance broker. You won't get the full discounted rate but shouldn't have to start off at the high beginner's rate either. You might find that insurance itself is cheaper, but the costs for maintaining and running your car will definitely be higher in Germany. Be prepared for a real shock the first time you fill up the gas tank. The closest gas station to me is currently selling regular unleaded for 1.489 euro/litre.
Sorry I can't help with your health insurance costs since I'm not with AOK. But search a little and you'll find lots of info here on the site.
Also be warned that many landlords tend to under-estimate utility and other costs aside from basic rent. (water, electricity etc.) These "nebenkosten" can end up being an unhappy suprise at the end of the year when actual use is compared to the estimate. For the first two or three months, keep an eye on hot water and electricity use, and then perhaps adjust your monthly payment up a bit (or your savings) so you don't get stuck with an unexpected big bill at the end of the year.
Good luck with the move!